Mathias R. Jessen's helpful answer shows how to save your function's definition to a custom file that you can dot-source on demand in future sessions.
However, there is a file that is dot-sourced automatically when a PowerShell session starts (unless explicitly suppressed with -NoProfile via the PowerShell CLI): your $PROFILE file, and that's where customizations of your sessions - such as custom functions and aliases - are typically stored.
Therefore, if you add your function to your $PROFILE file, it automatically becomes available in future sessions too.
You can open $PROFILE in your text editor or, building on Mathias' technique, add the function programmatically, as follows, which ensures on-demand creation of the file and its parent directory (on a pristine machine, neither exists):
# Make sure the $PROFILE file exists.
If (-not (Test-Path $PROFILE)) { $null = New-Item -Force $PROFILE }
# Append the function definition to it.
@"
function Restart-PowerShell {
${function:Restart-PowerShell}
}
"@ | Add-Content $PROFILE
Note: To reload your profile mid-session after having modified $PROFILE, use . $PROFILE.